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random-grid lists: Plotting


Does anybody know that wether is it possible (and how) to
plot a 3D->1D function, when I have this function only numerically,
on random grid?  (In this case the Interpolation[] does not seems to work)
    (random grid = not rectangular grid)
Or in more simple case, a random grid is this:

In[1]:= data={ {0,0,0},{0,1,1},{1,0,1},
              {1,1,2},{0.25,0,0.25},{0.5,0,0.5} }
In[2]:= f=Interpolation[data]
   Coordinate 0.5 in data point {0.5, 0, 0.5}
     does not match the corresponding coordinate in {0, 0.25, 1}.

plese help.
ps: Do you think I can Fourier transform this?
does that help?

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